Network Analysis

Distance in GIS

• Review: how can distance be measured in a GIS context?

Types of distance in GIS

• Euclidean (planar) distance
• Manhattan distance
• Geodesic distance
• Network distance

Euclidean vs. Manhattan distance

Source: Wikipedia

Geodesic distance

Source: Esri

Distance in urban/business analysis

Network distance

• Core principle: determination of shortest distance between two points along a network
• Based on topological relationships between features

‘Cost’ and network analysis

Source: Bolstad, GIS Fundamentals

The Dijkstra algorithm

Source: Bolstad, GIS Fundamentals

Linear referencing

• A type of alternative datum for determining relative locations
• Linear referencing system: features stored with reference to line features (e.g. I-35W, mile 15.6); can be used instead of x, y coordinates

Topology

Source: Bolstad, GIS Fundamentals

Other types of network analysis

• Geometric networks

Source: Esri

Components of a road network

• A linear reference (generally, a streets dataset)
• Some way to calculate a cost attribute along the network, e.g.;
• Distance: length of line segment
• Time: impedance to travel
• Information about characteristics of a road network

Time as a cost attribute

• How to calculate? Must have some ancillary information about travel speeds along roads
• Example: speed limit information; traffic profiles
• Basic formula: \(time = rate / distance\)
• Gets more complicated with traffic

Traffic in network analysis

Source: Esri

Traffic in ArcGIS

• Tutorial!

• Server URL: http://traffic.arcgis.com/arcgis

Network analysis and logistics

Video on UPS’s ORION system

Applications of network analysis

• Vehicle routing
• Service area (drive-time) analysis
• Closest facility analysis
• Location-allocation modeling
• Advanced business analytics

Vehicle routing

Service area analysis

• Tutorial!

Closest facility analysis

Location-allocation modeling

Source: Esri

Gravity modeling

In a GIS context, a gravity model can be specified as:

\[P_{ij} = \dfrac{W_i/D_{ij}^\alpha}{\sum_{i=1}^{n}(W_i/D_{ij}^\alpha)}\]

Where:

\(P_{ij}\) = the probability of customer \(j\) shopping at store \(i\);

\(W_i\) = some measure of the attractiveness of each store \(i\);

\(D_{ij}\) = the distance from customer \(j\) to store \(i\);

\(\alpha\) = a distance-decay parameter

Huff model

• Employs principles of gravity modeling to forecast customer demand, sales potential
• Implemented in Esri’s Business Analyst for Desktop

Image source

Network analysis beyond ArcGIS

• pgRouting: Adds routing functionality to PostgreSQL/PostGIS; can be integrated with QGIS
• Employs OpenStreetMap data

Want to do more?

Check out the suite of Esri Network Analyst tutorials here: